In magnetic-recording systems, consecutive sections experience different
signal to noise ratios (SNRs). To perform error correction over these systems,
one approach is to use an individual block code for each section. However, a
section affected by a lower SNR shows a weaker performance compared to a
section affected by a higher SNR. A commonly used technique is to perform
interleaving across blocks to alleviate negative effects of varying SNR.
However, this scheme is typically costly to implement and does not result in
the best performance. Spatially-coupled (SC) codes are a family of graph-based
codes with capacity approaching performance and low latency decoding. An SC
code is constructed by partitioning an underlying block code to several
component matrices, and coupling copies of the component matrices together. The
contribution of this paper is threefold. First, we present a new partitioning
technique to efficiently construct SC codes with column weights 4 and 6.
Second, we present an SC code construction for channels with SNR variation. Our
SC code construction provides local error correction for each section by means
of the underlying codes that cover one section each, and simultaneously, an
added level of error correction by means of coupling among the underlying
codes. Consequently, and because of the structure of SC codes, more reliable
sections can help unreliable ones to achieve an improved performance. Third, we
introduce a low-complexity interleaving scheme specific to SC codes that
further improves their performance over channels with SNR variation. Our
simulation results show that our SC codes outperform individual block codes by
more than 1 and 2 orders of magnitudes in the error floor region compared to
the block codes with and without regular interleaving, respectively. This
improvement is more pronounced by increasing the memory and column weight.

Generalized frequency division multiplexing (GFDM) is considered a
non-orthogonal waveform and known to encounter difficulties when using in the
spatial multiplexing mode of multiple-input-multiple-output (MIMO) scenario. In
this paper, a class of GFDM prototype filters, under which the GFDM system is
free from inter-subcarrier interference, is investigated, enabling
frequency-domain decoupling in the processing at the GFDM receiver. An
efficient MIMO-GFDM detection method based on depth-first sphere decoding is
then proposed with such class of filters. Numerical results confirm a
significant reduction in complexity, especially when the number of subcarriers
is large, compared with existing methods presented in recent years.

Age of information (AoI) is a recently proposed metric for measuring
information freshness. AoI measures the time that elapsed since the last
received update was generated. We consider the problem of minimizing average
and peak AoI in wireless networks under general interference constraints. When
fresh information is always available for transmission, we show that a
stationary scheduling policy is peak age optimal. We also prove that this
policy achieves average age that is within a factor of two of the optimal
average age. In the case where fresh information is not always available, and
packet/information generation rate has to be controlled along with scheduling
links for transmission, we prove an important separation principle: the optimal
scheduling policy can be designed assuming fresh information, and
independently, the packet generation rate control can be done by ignoring
interference. Peak and average AoI for discrete time G/Ber/1 queue is analyzed
for the first time, which may be of independent interest.

Age of Information (AoI), measures the time elapsed since the last received
information packet was generated at the source. We consider the problem of AoI
minimization for single-hop flows in a wireless network, under pairwise
interference constraints and time varying channel. We consider simple, yet
broad, class of distributed scheduling policies, in which a transmission is
attempted over each link with a certain attempt probability. We obtain an
interesting relation between the optimal attempt probability and the optimal
AoI of the link, and its neighboring links. We then show that the optimal
attempt probabilities can be computed by solving a convex optimization problem,
which can be done distributively.

Age of information (AoI), defined as the time elapsed since the last received
update was generated, is a newly proposed metric to measure the timeliness of
information updates in a network. We consider AoI minimization problem for a
network with general interference constraints, and time varying channels. We
propose two policies, namely, virtual-queue based policy and age-based policy
when the channel state is available to the network scheduler at each time step.
We prove that the virtual-queue based policy is nearly optimal, up to a
constant additive factor, and the age-based policy is at-most factor 4 away
from optimality. Comparing with our previous work, which derived age optimal
policies when channel state information is not available to the scheduler, we
demonstrate a 4 fold improvement in age due to the availability of channel
state information.

In this paper, the line spectral estimation (LSE) problem with multiple
measurement vectors (MMVs) is studied utilizing the Bayesian methods. Motivated
by the recently proposed variational line spectral estimation (VALSE) method,
we extend it to deal with the MMVs setting, which is especially important in
array signal processing. The VALSE method can automatically estimate the model
order and nuisance parameters such as noise variance and weight variance. In
addition, by approximating the probability density function (PDF) of the
frequencies with the mixture of von Mises PDFs, closed-form update equation and
the uncertainty degree of the estimates can be obtained. Interestingly, we find
that the VALSE with MMVs can be viewed as applying the VALSE with single
measurement vector (SMV) to each snapshot, and combining the intermediate data
appropriately. Furthermore, the proposed prior distribution provides a good
interpretation of tradeoff between grid and off-grid based methods. Finally,
numerical results demonstrate the effectiveness of the VALSE method, compared
to the state-of-the-art methods in the MMVs setting.

We consider a general multi-user Mobile Cloud Computing (MCC) system where
each mobile user has multiple independent tasks. These mobile users share the
computation and communication resources while offloading tasks to the cloud. We
study both the conventional MCC where tasks are offloaded to the cloud through
a wireless access point, and MCC with a computing access point (CAP), where the
CAP serves both as the network access gateway and a computation service
provider to the mobile users. We aim to jointly optimize the offloading
decisions of all users as well as the allocation of computation and
communication resources, to minimize the overall cost of energy, computation,
and delay for all users. The optimization problem is formulated as a non-convex
quadratically constrained quadratic program, which is NP-hard in general. For
the case without a CAP, an efficient approximate solution named MUMTO is
proposed by using separable semidefinite relaxation (SDR), followed by recovery
of the binary offloading decision and optimal allocation of the communication
resource. To solve the more complicated problem with a CAP, we further propose
an efficient three-step algorithm named MUMTO-C comprising of generalized MUMTO
SDR with CAP, alternating optimization, and sequential tuning, which always
computes a locally optimal solution. For performance benchmarking, we further
present numerical lower bounds of the minimum system cost with and without the
CAP. By comparison with this lower bound, our simulation results show that the
proposed solutions for both scenarios give nearly optimal performance under
various parameter settings, and the resultant efficient utilization of a CAP
can bring substantial cost benefit.

The rate flexibility and probabilistic shaping gain of $4$-dimensional
signaling is experimentally tested for short-reach, unrepeated transmission. A
rate granularity of 0.5 bits/QAM symbol is achieved with a distribution matcher
based on a simple look-up table.

There is an increase in usage of smaller cells or femtocells to improve
performance and coverage of next-generation heterogeneous wireless networks
(HetNets). However, the interference caused by femtocells to neighboring cells
is a limiting performance factor in dense HetNets. This interference is being
managed via distributed resource allocation methods. However, as the density of
the network increases so does the complexity of such resource allocation
methods. Yet, unplanned deployment of femtocells requires an adaptable and
self-organizing algorithm to make HetNets viable. As such, we propose to use a
machine learning approach based on Q-learning to solve the resource allocation
problem in such complex networks. By defining each base station as an agent, a
cellular network is modelled as a multi-agent network. Subsequently,
cooperative Q-learning can be applied as an efficient approach to manage the
resources of a multi-agent network. Furthermore, the proposed approach
considers the quality of service (QoS) for each user and fairness in the
network. In comparison with prior work, the proposed approach can bring more
than a four-fold increase in the number of supported femtocells while using
cooperative Q-learning to reduce resource allocation overhead.

We consider the variable-to-fixed length lossy source coding (VFSC) problem.
The optimal compression rate of the average length of variable-to-fixed source
coding, allowing a non-vanishing probability of excess-distortion
$\varepsilon$, is shown to be equal to $(1-\varepsilon)R(D)$, where $R(D)$ is
the rate-distortion function of the source. In comparison to the related
results of Koga and Yamamoto as well as Kostina, Polyanskiy, and Verd\'{u} for
fixed-to-variable length source coding, our results demonstrate an interesting
feature that variable-to-fixed length source coding has the same first-order
compression rate as fixed-to-variable length source coding.

We address centralized caching problem with unequal cache sizes. We consider
a system with a server of files connected through a shared error-free link to a
group of cache-enabled users where one subgroup has a larger cache size than
the rest. We investigate caching schemes with uncoded cache placement which
minimize the load of worst-case demands over the shared link. We propose a
caching scheme which improves upon existing schemes by either having a lower
worst-case load, or decreasing the complexity of the scheme while performing
within 1.1 multiplicative factor suggested by our numerical simulations.

In this paper, we address the symbol level precoding (SLP) design problem
under max-min SINR criterion in the downlink of multiuser multiple-input
single-output (MISO) channels. First, we show that the distance preserving
constructive interference regions (DPCIR) are always polyhedral angles (shifted
pointed cones) for any given constellation point with unbounded decision
region. Then we prove that any signal in a given unbounded DPCIR has a norm
larger than the norm of the corresponding vertex if and only if the convex hull
of the constellation contains the origin. Using these properties, we show that
the power of the noiseless received signal lying on an unbounded DPCIR is an
strictly increasing function of two parameters. This allows us to reformulate
the originally non-convex SLP max-min SINR as a convex optimization problem. We
discuss the loss due to our proposed convex reformulation and provide some
simulation results.

Comments: Single column, main text: 20 pages, full length with appendices: 32 pages. Includes pseudo-codes for all algorithms. Part of this work has been submitted to the 2018 IEEE International Symposium on Information Theory

Subjects:Information Theory (cs.IT); Quantum Physics (quant-ph)

Quantum error-correcting codes can be used to protect qubits involved in
quantum computation. This requires that logical operators acting on protected
qubits be translated to physical operators (circuits) acting on physical
quantum states. We propose a mathematical framework for synthesizing physical
circuits that implement logical Clifford operators for stabilizer codes.
Circuit synthesis is enabled by representing the desired physical Clifford
operator in $\mathbb{C}^{N \times N}$ as a partial $2m \times 2m$ binary
symplectic matrix, where $N = 2^m$. We state and prove two theorems that use
symplectic transvections to efficiently enumerate all symplectic matrices that
satisfy a system of linear equations. As an important corollary of these
results, we prove that for an $[\![ m,m-k ]\!]$ stabilizer code every logical
Clifford operator has $2^{k(k+1)/2}$ symplectic solutions. The desired physical
circuits are then obtained by decomposing each solution as a product of
elementary symplectic matrices. Our assembly of the possible physical
realizations enables optimization over them with respect to a suitable metric.
Furthermore, we show that any circuit that normalizes the stabilizer of the
code can be transformed into a circuit that centralizes the stabilizer, while
realizing the same logical operation. Our method of circuit synthesis can be
applied to any stabilizer code, and this paper provides a proof of concept
synthesis of universal Clifford gates for the $[\![ 6,4,2 ]\!]$ CSS code. We
conclude with a classical coding-theoretic perspective for constructing logical
Pauli operators for CSS codes. Since our circuit synthesis algorithm builds on
the logical Pauli operators for the code, this paper provides a complete
framework for constructing all logical Clifford operators for CSS codes.
Programs implementing our algorithms can be found at
https://github.com/nrenga/symplectic-arxiv18a.

This paper focuses on assessing the limitations in the direction-finding
process of radio sources with directional antennas in an urbanized environment,
demonstrating how signal source antenna parameters, such as beamwidth and
maximum radiation direction affect bearing accuracy in non-line-of-sight (NLOS)
conditions. These evaluations are based on simulation studies, which use
measurement-tested signal processing procedures. These procedures are based on
a multi-elliptical propagation model, the geometry of which is related to the
environment by the power delay profile or spectrum. The probability density
function of the angle of arrival for different parameters of the transmitting
antenna is the simulation result. This characteristic allows assessing the
effect of the signal source antenna parameters on bearing error. The obtained
results are the basis for practical correction bearing error and these show the
possibility of improving the efficiency of the radio source location in the
urbanized environment.

Multi-beam selection is one of the crucial technologies in hybrid beamforming
systems for frequency-selective fading channels. Addressing the problem in the
frequency domain facilitates the procedure of acquiring observations for analog
beam selection. However, it is difficult to improve the quality of the
contaminated observations at low SNR. To this end, this paper uses an idea that
the significant observations are sparse in the time domain to further enhance
the quality of signals as well as the beam selection performance. By exploiting
properties of channel impulse responses and circular convolutions in the time
domain, we can reduce the size of a Toeplitz matrix in deconvolution to
generate periodic true values of coupling coefficients plus random noise
signals. An arithmetic mean of these signals yields refined observations with
minor noise effects and provides more accurate sparse multipath delay
information. As a result, only the refined observations associated with the
estimated multipath delay indices have to be taken into account for the analog
beam selection problem.

We consider the problem of estimating the discrete clustering structures
under Sub-Gaussian Mixture Models. Our main results establish a hidden
integrality property of a semidefinite programming (SDP) relaxation for this
problem: while the optimal solutions to the SDP are not integer-valued in
general, their estimation errors can be upper bounded in terms of the error of
an idealized integer program. The error of the integer program, and hence that
of the SDP, are further shown to decay exponentially in the signal-to-noise
ratio. To the best of our knowledge, this is the first exponentially decaying
error bound for convex relaxations of mixture models, and our results reveal
the "global-to-local" mechanism that drives the performance of the SDP
relaxation.
A corollary of our results shows that in certain regimes the SDP solutions
are in fact integral and exact, improving on existing exact recovery results
for convex relaxations. More generally, our results establish sufficient
conditions for the SDP to correctly recover the cluster memberships of
$(1-\delta)$ fraction of the points for any $\delta\in(0,1)$. As a special
case, we show that under the $d$-dimensional Stochastic Ball Model, SDP
achieves non-trivial (sometimes exact) recovery when the center separation is
as small as $\sqrt{1/d}$, which complements previous exact recovery results
that require constant separation.

We establish the fundamental limits of lossless analog compression by
considering the recovery of arbitrary m-dimensional real random vectors x from
the noiseless linear measurements y=Ax with n x m measurement matrix A. Our
theory is inspired by the groundbreaking work of Wu and Verdu (2010) on almost
lossless analog compression, but applies to the nonasymptotic, i.e., fixed-m
case, and considers zero error probability. Specifically, our achievability
result states that, for almost all A, the random vector x can be recovered with
zero error probability provided that n > K(x), where the description complexity
K(x) is given by the infimum of the lower modified Minkowski dimensions over
all support sets U of x. We then particularize this achievability result to the
class of s-rectifiable random vectors as introduced in Koliander et al. (2016);
these are random vectors of absolutely continuous distribution---with respect
to the s-dimensional Hausdorff measure---supported on countable unions of
s-dimensional differentiable manifolds. Countable unions of differentiable
manifolds include essentially all signal models used in compressed sensing
theory, in spectrum-blind sampling, and in the matrix completion problem.
Specifically, we prove that, for almost all A, s-rectifiable random vectors x
can be recovered with zero error probability from n>s linear measurements. This
threshold is, however, found not to be tight as exemplified by the construction
of an s-rectifiable random vector that can be recovered with zero error
probability from n<s linear measurements. This leads us to the introduction of
the new class of s-analytic random vectors, which admit a strong converse in
the sense of n greater than or equal to s being necessary for recovery with
probability of error smaller than one. The central conceptual tool in the
development of our theory is geometric measure theory.

Quantum addition channels have been recently introduced in the context of
deriving entropic power inequalities for finite dimensional quantum systems. We
prove a reverse entropy power equality which can be used to analytically prove
an inequality conjectured recently for arbitrary dimension and arbitrary
addition weight. We show that the relative entropic difference between the
output of such a quantum additon channel and the corresponding classical
mixture quantitatively captures the amount of coherence present in a quantum
system. This new coherence measure admits an upper bound in terms of the
relative entropy of coherence and is utilized to formulate a state-dependent
uncertainty relation for two observables. Our results may provide deep insights
to the origin of quantum coherence for mixed states that truly come from the
discrepancy between quantum addition and the classical mixture.

We study a natural Wasserstein gradient flow on manifolds of probability
distributions with discrete sample spaces. We derive the Riemannian structure
for the probability simplex from the dynamical formulation of the Wasserstein
distance on a weighted graph. We pull back the geometric structure to the
parameter space of any given probability model, which allows us to define a
natural gradient flow there. In contrast to the natural Fisher-Rao gradient,
the natural Wasserstein gradient incorporates a ground metric on sample space.
We discuss implementations following the forward and backward Euler methods. We
illustrate the analysis on elementary exponential family examples.

Comments: This version forms a substantive extension of Version 1. We provide a construction of MDS codes that support optimal cooperative repair for all admissible parameters. This resolves the general problem of constructing codes for cooperative repair with minimum repair bandwidth